Quantum measurements constrained by the third law of thermodynamics

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Abstract

While quantum theory dictates that the act of measurement must perturb at least some property of the measured system, it does allow for measurements that are minimally invasive. Indeed, the existence of such measurements plays a crucial role in several foundational questions pertaining to quantum reality. For example, the Einstein-Podolsky-Rosen criterion of physical reality implicitly assumes the existence of “ideal” measurements which do not perturb the state of the measured system whenever the measurement outcome can be predicted with certainty. On the other hand, “repeatable” measurements, for which the same outcome is guaranteed to obtain under repeated measurements, are necessary if a property can be said to exist in the system after measurement, even if it does not exist prior to it. Given that the measurement process must ultimately result from a physical interaction between the measured system and a given measuring apparatus, however, the existence of such minimally invasive measurements may be in conflict with fundamental laws of nature. For example, the Wigner-Araki-Yanase theorem states that when the measurement interaction obeys a conservation law, then only observables that commute with the conserved quantity admit a repeatable measurement. In this work, we address the compatibility of several classes of minimally invasive measurements with another fundamental law of nature: the third law of thermodynamics, which states that no system can be cooled to absolute zero temperature. It is shown that while the third law prohibits ideal and repeatable measurements for all observables, the weaker notions of "approximately" ideal and "first-kind" measurements may be achieved, but only if the measured observable does not admit definite values. Our findings warrant a re-evaluation for the assignment of reality to quantum systems, and in particular lend support to the “Unsharp Reality” project of Busch and Jaeger.